The short answer is that you cannot sit the exams after the 31st March.
You cannot obtain the MCDST exam after this, but you can still sit exam 70-621 or 70-682 to upgrade this.
Microsoft have not released retiring exam information for June 30, see here: http://www.microsoft.com/learning/en/us/certification/exam-dev.aspx#tab4
There is a high chance that that the upgrade exams 621 and 682 will retire on June 30 (Not confirmed) as Microsoft tend to retire upgrade exams soon after retiring the certification.
My best guess is that you can obtain MCDST before March 31, but must upgrade before June 30 if you want to use the upgrade path's available.
Jarad, MCITP, Brisbane Australia